Mechanistic understanding of the correlation between structure and dynamics of liquid carbonate electrolytes: impact of polarization.

Liquid electrolyte design and modelling is an essential part of the development of improved lithium ion batteries. For mixed organic carbonates (ethylene carbonate (EC) and ethyl-methyl carbonate (EMC) mixtures)-based electrolytes with LiPF6 as salt, we have compared a polarizable force field with the standard non-polarizable force field with and without charge rescaling to model the structural and dynamic properties. The result of our molecular dynamics simulations shows that both polarizable and non-polarizable force fields have similar structural factors, which are also in agreement with X-ray diffraction experimental results. In contrast, structural differences are observed for the lithium neighborhood, while the lithium-anion neighbourhood is much more pronounced for the polarizable force field. Comparison of EC/EMC coordination statistics with Fourier transformed infrared spectroscopy (FTIR) shows the best agreement for the polarizable force field. Also for transport quantities such as ionic conductivities, transference numbers, and viscosities, the agreement with the polarizable force field is by far better for a large range of salt concentrations and EC : EMC ratios. In contrast, for the non-polarizable variants, the dynamics are largely underestimated. The excellent performance of the polarizable force field is explored in different ways to pave the way to a realistic description of the structure-dynamics relationships for a wide range of salt and solvent compositions for this standard electrolyte. In particular, we can characterize the distinct correlation terms between like and unlike ions, relate them to structural properties, and explore to which degree the transport in this electrolyte is mass or charge limited.

Sparse inference and active learning of stochastic differential equations from data.

Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and neural-network-based inference for empirical modelling, a physical interpretation of the results often remains challenging. Here, we focus on direct inference of governing differential equations from data, which can be formulated as a linear inverse problem. A Bayesian framework with a Laplacian prior distribution is employed for finding sparse solutions efficiently. The superior accuracy and robustness of the method is demonstrated for various cases, including ordinary, partial, and stochastic differential equations. Furthermore, we develop an active learning procedure for the automated discovery of stochastic differential equations. In this procedure, learning of the unknown dynamical equations is coupled to the application of perturbations to the measured system in a feedback loop. We show that active learning can significantly improve the inference of global models for systems with multiple energetic minima.